Maybe 5四奔. Improves the position on the column.
Chu Shogi Endgame Study #1

Figured it out. ☖5四奔☗2八横☖5五奔☗1八横☖4五奔☗2八横☖4六奔☗投了
☖5四奔☗3八横☖3十と寄☗7八麒☖5七奔☗12八横☖10七獅☗8八横☖10八と☗1八横☖4八と☗1九横☖3九と引☗1十横☖3十象☗1十一横☖1七奔☗5十一横☖4十と☗投了
So Gote is clearly winning unless either: a) there is a hole in the castle; or b) Sente trades off another tokin for a piece before this endgame is reached. It may still be winning, but that is more unclear.

Another potential goal for Sente. 3 pieces traded off each, including the kirin. Shifted castle. What do you think about this?
Both simplified endgame diagrams have removed 1 tokin from Gote so that any proof of a winning position would be solidified. You could also consider the above diagram with a tokin on 4八.
This already looks more drawish, even with an added tokin. And Sente is much more free to trade off his 横.

I would also consider it a draw. I thought about what the best move would be, but you can only trade off your tokin, with which you will not be able to deliver mate in the end. There are to much defending step movers.

It's not trivial to defend this. Suppose there was a tokin that got traded off for the side mover, which sente would had to have done in any case.
Sente to move

5十虎?
Defends against the と, while not letting the 獅 getting near, or making any unnecessary room for the enemy.

Seems okay in the short term. But in the long term, sente will need to push closer to the corner to be able to eventually hold a 3 pieces vs lion endgame. It feels counterproductive to move any piece away from the corner. The tokin will get a piece. That is not avoidable. My greatest concern as sente would be to prevent the lion from flanking on the right.
My first thought was 3十金. But then 5十一奔 looks very scary.

I don't see a solution. Whatever piece moves to the right side, opens up a way to be punished, so it seems to me...

For the sake of analysis, any arrangement of pieces within the castle could be looked at. I just picked one that looked solid.
In the current position, I like 3十二玉

☗3十二玉☖2九獅☗2十一象
A☖7十と☗4十二虎寄
B☖4四奔☗3十一虎
I don't see the point of 2九獅 immediately when all the combination potential remains at sente's left side.

I am sorry but novadays I don't have the time and energy for this difficult examples. I really appreciate it and want to get better in chu shogi, but as you see I need long to answer. Therefore I will stop for now and will continue practice in some months, when I have more time, if you still like to. Sorry for that. I will still finish my game with evert though, which is somehow easier for me then endgame.
☖6七獅☗7九麒☖4八と☗7十二玉 If ☖7八獅 then just ☗4八横 and you lost a tokin for nothing